One avenue by which quantitative easing could raise money expenditures on domestic product is through a lower exchange rate. The lower exchange rate will tend to result in an expansion of exports and a decrease in imports. The decrease imports should be associated with an expansion in the demand for the products of import competing industries.
If the foreigners respond to the quantitative easing with their own quantitative easing, then exchange rates will not change. Quantitative easing will still raise purchases in each and every country, including purchases of foreign products. Both imports and exports would rise as real output and real income recover. (This, of course, assumes that real expenditures is less than the productive capacity of the economy, which is the primary reason to undertake quantitative easing. If real expenditures are equal to the productive capacity of the economy, then money expenditures are at the appropriate level.)
Suppose that rather than responding with their own quantitative easing, foreign central banks prevent their exchange rates from rising by accumulating assets denonominated in the currency issued by the central bank underaking the quantitative easing, while selling off other types of assets. F or example, imagine that China restricts new loans to Chinese firms, and as old loans are repaid, purchases U.S. Treasury securities. In other words, China generates whatever net capital outflow is needed to avoid any increase in its exchange rate.
Unlike the scenario where competitive quantitive easing expands demand all over, and so results in expansions in both exports and imports for each country, here the pathway by which a lower exchange rate expands demand is closed, and there is no foreign quantitative easing to expand exports. The only pathway by which quantitative easing expands money expenditures is domestic purchases on domestic product. This simply means that more quantitative easing--a larger expansion in the quantity of money--is necessary to return money expenditures to the desired level.
Another way to see the "problem," is that the efforts of the foreign countries to avoid exchage rate appreciation without expanding money expenditures in their own countries--that is, sterilization--involves a decrease in the natural interest rate for the country undertaking the quantitative easing. The net capital inflow generated by the foreign central bank(s) is an addition to saving, and requires a lower level of interest rates for total saving to be balanced with investment.
My view is that a clear committment to a prompt return to a reasonble growth path for money expenditures will raise the natural interest rate. Any increase in expected inflation would further raise the nominal interest rate consistent with any natural interest rate. And so, the most likely scenario is that efforts by foreign central banks to keep their currencies from appreciating would simply dampen the increase in the nominal market interest rates consistent with money expenditures returning to and then remaining on the targetted growth path.
However, if those effects are ignored, so that the additional quantity of money simultaneously involves an expansion in the total demand for bonds, then an alternative perspective would be that a larger increase in the quantity of money also entails a larger decrease in some type of nominal interest rate. If it is assumed that quantitative easing involves the central bank purchasing short and safe assets, such as T-bills, and further, that the foreign central banks are also purchasing T-bills to keep their currencies from appreciating, and still further, that the yield on those T-bills has been driven to approximately zero, then perhaps the foreign central banks might be blamed for the failure of quantitative easing. If only the foreign central banks didn't purchase all of those T-bills, then their yield would be above zero and quantitative easing would work. Of course, so would conventional interest rate targeting.
But proposals for quantitative easing usually involve the purchase of assets that are not so so short or safe, in particular, longer term government bonds whose yields are not close to zero. And so, the bottom line is that the efforts of the foreign central banks to keep their currencies from appreciating by purchasing some kind of assets requires that the central bank undertaking the quantitative easing purchase a larger quantity of longer term or riskier assets than otherwise would be needed. With longer term assets, like 10 year government bonds, at the very least bearing more interest rate risk, the efforts of the foreign central banks are requiring the central bank undertaking quantitative easing to bear more risk than would otherwise be necessary.
To me, the obvious solution is for the yield on money to fall, and if necessary, to become negative. Since I strongly favor a growth path for money expenditures consistent with a stable price level on average, negative nominal interest rates on money is the obvious answer. If foreign central banks want to accumulate large amounts of safe and short assets, then the nominal yield on such assets should perhaps be negative. And, of course, that creates problems with the issue of zero-interest hand-to-hand currency.
To put it simply, if the central bank promises to issue zero-interest hand-to-hand currency on demand, and it is committed to a rule for noninflationary growth of money expenditures, then, it is possible that it will have to bear, at the very least, interest rate risk by borrowing short (issuing zero interest currency) and lending long. If foreign central banks accumulate assets, then this problem is exacerbated. If they can be brow-beaten into allowing their currencies to appreciate, then this "problem" is less severe.